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Proof step 11 from proof absexpt-avols-write (previous step)

v0 ∈ vols ↔ v0 ∈ avols[v, avols[v][m, leb]], apebs[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m < # avols[v], v ∈ avols, v0 ∈ vols → # vols[v0] = # avols[v, avols[v][m, leb]][v0] ∧ (∀ m1. (v0 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v0] → (vols[v0][m1] = unmapped → ¬ avols[v, avols[v][m, leb]][v0][m1].mapped?) ∧ ( vols[v0][m1] ≠ unmapped → avols[v, avols[v][m, leb]][v0][m1].mapped? ∧ avols[v, avols[v][m, leb]][v0][m1].data = apebs[vols[v0][m1].pnum].data ∧ apebs[vols[v0][m1].pnum].fill ≤ avols[v, avols[v][m, leb]][v0][m1].fill) ∧ (avols[v, avols[v][m, leb]][v0][m1] = erased → ¬ v0 × m1 ∈ q)), ∀ v1. (v1 ∈ vols ↔ v1 ∈ avols[v, avols[v][m, leb]]) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v, avols[v][m, leb]][v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v, avols[v][m, leb]][v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v, avols[v][m, leb]][v1][m1].mapped? ∧ avols[v, avols[v][m, leb]][v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v, avols[v][m, leb]][v1][m1].fill) ∧ (avols[v, avols[v][m, leb]][v1][m1] = erased → ¬ v1 × m1 ∈ q))) ⊦ v0 = v, (v0 ∈ vols ↔ v0 ∈ avols) ∧ ( v0 ∈ vols → # vols[v0] = # avols[v0] ∧ ( (v0 ≠ v ∨ m0 ≠ m) ∧ m0 < # vols[v0] → (vols[v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ (vols[v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = buf ∧ m2 ≤ avols[v0][m0].fill) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# vols[v0] = # avols[v0], apebs[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m0 < # avols[v0], m < # avols[v], v0 ∈ avols, v0 ∈ vols, v ∈ avols, ∀ m1. m1 < # avols[v0] → (vols[v0][m1] = unmapped → ¬ avols[v0][m1].mapped?) ∧ ( vols[v0][m1] ≠ unmapped → avols[v0][m1].mapped? ∧ avols[v0][m1].data = apebs[vols[v0][m1].pnum].data ∧ apebs[vols[v0][m1].pnum].fill ≤ avols[v0][m1].fill) ∧ (avols[v0][m1] = erased → ¬ v0 × m1 ∈ q), ∀ v1. (v1 ∈ vols ↔ v1 ∈ avols[v, avols[v][m, leb]]) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v, avols[v][m, leb]][v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v, avols[v][m, leb]][v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v, avols[v][m, leb]][v1][m1].mapped? ∧ avols[v, avols[v][m, leb]][v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v, avols[v][m, leb]][v1][m1].fill) ∧ (avols[v, avols[v][m, leb]][v1][m1] = erased → ¬ v1 × m1 ∈ q))) ⊦ v0 = v, (vols[v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ (vols[v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = buf ∧ m2 ≤ avols[v0][m0].fill) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ≠ v0 → avols[v0, evol][v] = avols[v]; (s)% ⊦ v ≠ v0 → (v ∈ avols[v0, evol] ↔ v ∈ avols); (s)